If the weather is close to minima and I expect a possible Go Around then I tell the passengers! "The weather is well within our limits to make an approach but if we dont see the runway by the prescribed point we will be climbing away again and may well be diverting to XXXX".
Then if you land they think what a great job you have done (true of course!) - if you Go Around it's no big surprise.
Obviously this doesnt cater for Go Arounds for other reasons (Tech/ATC etc) in which case an announcement will be made if and when circumstances allow.